An Advanced Weighted Levy Distribution: Statistical Properties and Application

Abstract

In order to model price variations in market, finance engineers may employ the concept of Levy distribution. The slow fall off of  the Levy  distribution model is a good match after price changes. In this paper, a new weighted model is introduced which would be obtained by assigning weights to Levy distribution. This work provides an insight to some basic distributional properties of this distributions such as Moments, moment generating function, Skewness, kurtosis, Shannon’s entropy etc. Maximum likelihood estimation and method of moments are employed to estimate the model parameters. For the purpose of illustration the proposed model would be applied to the real data set.

Keywords: Levy distribution, weighted distribution, Maximum likelihood estimation and Shannon’s entropy.